Details

sample32.0ms

Algorithm

intervals

Results

8.0ms	29×	body	2560	valid
6.0ms	185×	body	80	valid
3.0ms	14×	body	5120	valid
3.0ms	17×	body	1280	valid
1.0ms	7×	body	640	valid
0.0ms	2×	body	320	valid
0.0ms	2×	body	160	valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	8
1	28	8
2	36	8
3	44	8
4	46	8
5	46	8

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.2b

localize10.0ms

Local error

Found 2 expressions with local error:

0.4b	(- (sqrt (+ (* re re) (* im im))) re)
32.1b	(sqrt (+ (* re re) (* im im)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
18×	`prod-diff`
17×	`add-cube-cbrt`
16×	`sqrt-prod`
6×	`fma-neg`
4×	`add-log-exp`
3×	`pow1`
2×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u` `difference-of-squares`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip--` `flip-+` `hypot-def` `distribute-lft-out--`

Counts

2 → 59

Calls

2 calls:

21.0ms	(- (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series83.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(- (sqrt (+ (* re re) (* im im))) re)
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify105.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 3 (99.0ms)

Iter	Nodes	Cost
0	211	590
1	687	366
2	3279	321
3	5001	295

prune144.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 8.8b

localize8.0ms

Local error

Found 1 expressions with local error:

0.4b	(- (hypot re im) re)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`prod-diff`
8×	`add-cube-cbrt`
3×	`fma-neg` `add-log-exp`
1×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 28

Calls

1 calls:

3.0ms

(- (hypot re im) re)

series58.0ms

Counts

1 → 3

Calls

1 calls:

58.0ms

(- (hypot re im) re)

simplify46.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (43.0ms)

Iter	Nodes	Cost
0	119	199
1	333	125
2	1490	116
3	5001	85

prune73.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 8.8b

localize11.0ms

Local error

Found 1 expressions with local error:

17.3b

(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

series136.0ms

Counts

1 → 3

Calls

1 calls:

136.0ms

(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

simplify52.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 3 (14.0ms)

Iter	Nodes	Cost
0	48	100
1	133	85
2	439	82
3	1931	78
4	5001	78

prune59.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 8.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))
17.0b	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- re))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

0.0ms	(cbrt (hypot re im))
0.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
0.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- re))

series449.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(cbrt (hypot re im))
104.0ms	(cbrt (hypot re im))
105.0ms	(cbrt (hypot re im))
135.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- re))

simplify136.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 4 (129.0ms)

Iter	Nodes	Cost
0	84	329
1	188	287
2	663	279
3	3464	272
4	5001	263

prune194.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 8.7b

regimes174.0ms

Accuracy

34.6% (4.0b remaining)

Error of 11.2b against oracle of 7.2b and baseline of 13.4b

bsearch39.0ms

Steps

Iters	Range		Point
6	47183757994.54101	459530176245.3387	98254381358.47543

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	13
1	30	13
2	30	13

end0.0ms

sample693.0ms

Algorithm

intervals

Results

208.0ms	6004×	body	80	valid
144.0ms	741×	body	2560	valid
78.0ms	480×	body	1280	valid
70.0ms	296×	body	5120	valid
34.0ms	257×	body	640	valid
13.0ms	142×	body	320	valid
5.0ms	80×	body	160	valid